A mathematical model can estimate the probability that variants of SARS-CoV-2 are no longer circulating when lockdown restrictions are eased.
Imagine that a new vaccine-resistant variant of SARS-CoV-2 is freely circulating in an island in Denmark – such as Bornholm.
Further, imagine that the government wants to prevent SARS-CoV-2 from being transmitted to the rest of Denmark by simply halting all travel to and from Bornholm.
How long should the public authorities wait after the last positive PCR test for the variant on Bornholm before they can be reasonably sure that the variant is extinct and thus no longer poses a threat? When can the authorities safely allow travel to and from Bornholm again?
An algorithm developed in Denmark can answer these questions.
“It can estimate the probability that such variants are extinct when lockdown restrictions are eased,” explains a researcher behind the new algorithm, Martin Bøgsted, Professor, Department of Clinical Medicine, Aalborg University.
The research on the algorithm has been published in Scientific Reports.
Lockdown in northern Denmark
The development of the mathematical model was triggered by the mink variants of SARS-CoV-2 accounting for 20–60% of all positive PCR tests in northern Denmark. In addition, 11 cases of the special Cluster-5 mink variant had been discovered. This was a variant of concern to Statens Serum Institut because the variant might be resistant to the vaccines that were being developed. Seven municipalities were therefore locked down for 14 days in November 2020.
However, long before the 14 days of restrictions began, the Cluster-5 mink variant positive samples had disappeared from the overall positive tests for SARS-CoV-2.
However, not everyone was tested and not all positive samples were screened for the Cluster 5 mink variant. The question then was how sure could the authorities be that it was extinct?
The daily newspaper Berlingske also asked this question in November 2020.
When the media heard about the COVID-19-CTRL interdisciplinary project, which dealt specifically with mathematical models for controlling epidemics, they naturally reached out to the researchers behind the project. One of them, Martin Bøgsted, explains:
“We were locked down because we were surrounded by mink farms, and we were calculating how sure we could be that the mink variant had disappeared. Our initial calculations turned out to be too simple, so we developed this model, which can provide a better estimate of the probability that a virus variant is extinct,” he says.
The question is how certain the authorities want to be
The researchers include many parameters in the model that influence the probability that a variant is circulating.
These parameters include the population size in the study area, the number of sequenced individuals, the recovery time, the reproduction number and the initial number of people infected by the variant.
If one case of the examined variant is found, additional calculations are unnecessary, because the variant is not extinct.
The researchers retrospectively calculated the probability that the Cluster-5 mink variant was no longer circulating after the restrictions were lifted in northern Denmark: about 40% at that time.
“The number is, however, very uncertain since we only based our calculations on publicly available data. For example, we could not consider the specific efforts to find infected people,” says Martin Bøgsted.
“The question is how certain the authorities want to be before opening up,” Martin Bøgsted continues.
Potential new variants
One can reasonably ask whether retroactively examining the probability that virus variants are extinct is useful, but the model can also examine probabilities in real time.
In Cyprus, a new SARS-CoV-2 variant was thought to have arisen recently: Deltacron, a combination of the delta and omicron variants (this turned out to be an error).
If the new variant had arisen and the Cyprus government decided to lock down the country until it became extinct, they would have to estimate the probability that it would not circulate any longer, even after it had not been seen in test samples for some time.
The model could be used for this purpose and is available here.
“You can also invert the question and then ask how long you have to test for negative results to be 100% sure the virus is extinct. Just because everyone tests negative one day does not mean that the virus has disappeared. Our model can determine how many days you need to have exclusively negative answers before you are as confident as you choose to be. In addition, the model can also be used for future pandemics,” concludes Martin Bøgsted.
